Differential privacy: There have been a number of research results on differential privacy. Zhu et al. [1]} developed a distributed private online algorithm using a weight-balancing technique over time-varying undirected networks. Employing the Laplacian mechanism, a differential privacy version of the online subgradient-push algorithm [2]} is presented in [3]} for time-varying directed networks. In [1]}, [3]}, only the unconstrained optimization problems are considered. For constrained problems, by adopting the Laplace noise to the online version of the projected subgradient algorithm [6]}, Xiong et al. [7]} proposed a subgradient rescaling privacy-preserving algorithm over fixed directed networks. Moreover, Han et al. [8]} considered a privacy version of the work [9]} by adding perturbation to the data flow in communication channels. In [10]}, a differential privacy by functional perturbation is achieved, but it is limited due to the requirement of squared integrability on the objective functions.
